For the 25th anniversary of 6 nimmt!, publisher AMIGO held a design contest to add something new to the game.
Guillaume from France submitted the winning entry, which works like this: At the start of play, place the 6 nimmt!: Even/Odd card to the left of the row with the lowest card, flipping the card so that its even/odd status matches the adjacent card, e.g. 13 - Odd. As long as this card is next to this row, only odd cards can be played into it — which means you might be forced to play into a different row!
When any row is claimed, the player takes the five cards from that row, starts a new row with their sixth card, then moves the even/odd card to one of the other three rows, specifically the row with the lowest card in its rightmost position. Flip the even/odd card as needed to match the even/odd state of this numbered card.